If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?
This is from the GMAT Prep 1. Can someone please walk me through this?
MIT_Aspirant wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?
This is from the GMAT Prep 1. Can someone please walk me through this?
Raj wrote:LHS:
2^x(1- 1/4) = 2^x(3/2^2) = 3*2^(x-4). Now equate to RHS 3*2^(x-4) = 3*(2)^13, which means x-4 = 13, x=17.
-Raj.MIT_Aspirant wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?
This is from the GMAT Prep 1. Can someone please walk me through this?
Priyanka wrote:Instead of focusing on the LHS , we can try and simplify the RHS
LHS = 3 * 2^13
can be written as (2^2 - 1) * 2^13.
= 2^15 - 2^13.
now RHS = 2^x - 2^(x-2) = LHS = 2^15 - 2^13
therefore x = 15.
benkriger wrote:2x - 2^(x-2) = 3(2^13), what is x?
1) We can see from the statement that we are going to be working with the number 2 raised to a power. This is important, because there are patterns when taking the number 2 to a power.
2) Lets examine the LHS 2^x - 2^(x-2) by picking numbers and looking for a pattern.
-If we let x equal 4, then we get (2^4) - (2^2) = (16)-(4) = 12
-Lets do one more number just to make sure the pattern holds. Let x equal 5. Then we have (2^5) - (2^3) = (32)-(8) = 24
-Now what do we realize about the numbers 12 and 24? Well at first look you may not be sure. But looking at the RHS of the equation, you can see that they represented the right side as three times the number two to a power. So lets try breaking down each of these numbers into that pattern. 12=3*4 and we can break that down into 12= 3*2*2 and then we can simplify that into 12 =3*2^2. Do the same thing with the 24=3*8 which also means 24=3*2*2*2 and then finally 24=3*2^3.
What do we notice? If x=4, our equation was 3*2^2 and if x=5, we had 3*2^3. Both of these equations is simply 3*2^(x-2).
3)
We we now rearranged the equation to: 3*2^(x-2)=3*2^13 and now set x-2=13 and solve for x, and X=15.